Rectangular Hall-Littlewood symmetric functions and a specific spin character

We derive the Schur function identities coming from the tensor products of the spin representations of the symmetric group Sn. We deal with the tensor products of the basic spin representation V (n) and any spin representation V λ (λ ∈ SP (n)). The characteristic map of the tensor product ζn ⊗ ζλ is described by Stembridge[4] for the case of odd n. We consider the case n is even

Brauer-Schur functions

A new class of functions is studied. We define the Brauer-Schur functions $B^{(p)}_{\lambda}$ for a prime number $p$, and investigate their properties. We construct a basis for the space of symmetric functions, which consists of products of $p$-Brauer-Schur functions and Schur functions. We will see that the transition matrix from the natural Schur function basis has some interesting numerical properties

Quantum Sylvester-Franke Theorem

A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GLq (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturall

Virasoro Action on Schur Q-function (Women in Mathematics)

Schur Q-function was introduced by Schur as a symmetric polynomial describing the irreducible index of the projective representation of a symmetric group. A formula for Schur Qfunctions is presented which describes the action of the Virasoro operators. For strict partition, we prove a formula for each LkQλ. and L_kQλ. (k ≥ 1), where Lk is the Virasoro operator. The present paper is a résumé of [1] and [2]

Bile pigments in emergency and critical care medicine

Bile pigments, such as bilirubin and biliverdin, are end products of the heme degradation pathway in mammals and are widely known for their cytotoxic effects. However, recent studies have revealed that they exert cytoprotective effects through antioxidative, anti-inflammatory, and immunosuppressive properties. All these mechanisms are indispensable in the treatment of diseases in the field of emergency and critical care medicine, such as coronary ischemia, stroke, encephalomyelitis, acute lung injury/acute respiratory distress syndrome, mesenteric ischemia, and sepsis. While further research is required before the safe application of bile pigments in the clinical setting, their underlying mechanisms shed light on their utilization as therapeutic agents in the field of emergency and critical care medicine. This article aims to summarize the current understanding of bile pigments and re-evaluate their therapeutic potential in the diseases listed above

Association of Japan Coma Scale score on hospital arrival with in-hospital mortality among trauma patients

BACKGROUND: The Japan Coma Scale (JCS) score has been widely used to assess patients' consciousness level in Japan. JCS scores are divided into four main categories: alert (0) and one-, two-, and three-digit codes based on an eye response test, each of which has three subcategories. The purpose of this study was to investigate the utility of the JCS score on hospital arrival in predicting outcomes among adult trauma patients. METHODS: Using the Japan Trauma Data Bank, we conducted a nationwide registry-based retrospective cohort study. Patients 16 years old or older directly transported from the trauma scene between January 2004 and December 2017 were included. Our primary outcome was in-hospital mortality. We examined outcome prediction accuracy based on area under the receiver operating characteristic curve (AUROC) and multiple logistic regression analysis with multiple imputation. RESULTS: A total of 222,540 subjects were included; their in-hospital mortality rate was 7.1% (n = 15,860). The 10-point scale JCS and the total sum of Glasgow Coma Scale (GCS) scores demonstrated similar performance, in which the AUROC (95% CIs) showed 0.874 (0.871-0.878) and 0.878 (0.874-0.881), respectively. Multiple logistic regression analysis revealed that the higher the JCS score, the higher the predictability of in-hospital death. When we focused on the simple four-point scale JCS score, the adjusted odds ratio (95% confidence intervals [CIs]) were 2.31 (2.12-2.45), 4.81 (4.42-5.24), and 27.88 (25.74-30.20) in the groups with one-digit, two-digit, and three-digit scores, respectively, with JCS of 0 as a reference category. CONCLUSIONS: JCS score on hospital arrival after trauma would be useful for predicting in-hospital mortality, similar to the GCS score